1 Answer

Abhishek Asthana · Answer 1 · 2021-09-16T09:57:49+0000

Answer: 5 years

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

$t=(2.303)/(k)\log(a)/(a-x)$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant = x

a - x = amount left after decay process =
(x)/(16)

a) for calculating k

$20=(2.303)/(k)\log(x)/((x)/(16))$

$k=(2.303)/(20)\log{16}$

k=0.138years^(-1)

b) for calculating half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{(1)/(2)}=(0.693)/(0.138years^(-1))$

$t_{(1)/(2)}=5years$

Thus its half life is 5 years

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